Multiclass Alpha Integration of Scores from Multiple Classifiers.

Alpha integration methods have been used for integrating stochastic models and fusion in the context of detection (binary classification). Our work proposes separated score integration (SSI), a new method based on alpha integration to perform soft fusion of scores in multiclass classification problems, one of the most common problems in automatic classification. Theoretical derivation is presented to optimize the parameters of this method to achieve the least mean squared error (LMSE) or the minimum probability of error (MPE). The proposed alpha integration method was tested on several sets of simulated and real data. The first set of experiments used synthetic data to replicate a problem of automatic detection and classification of three types of ultrasonic pulses buried in noise (four-class classification). The second set of experiments analyzed two databases (one publicly available and one private) of real polysomnographic records from subjects with sleep disorders. These records were automatically staged in wake, rapid eye movement (REM) sleep, and non-REM sleep (three-class classification). Finally, the third set of experiments was performed on a publicly available database of single-channel real electroencephalographic data that included epileptic patients and healthy controls in five conditions (five-class classification). In all cases, alpha integration performed better than the considered single classifiers and classical fusion techniques.

A New Surrogating Algorithm by the Complex Graph Fourier Transform (CGFT).

The essential step of surrogating algorithms is phase randomizing the Fourier transform while preserving the original spectrum amplitude before computing the inverse Fourier transform. In this paper, we propose a new method which considers the graph Fourier transform. In this manner, much more flexibility is gained to define properties of the original graph signal which are to be preserved in the surrogates. The complex case is considered to allow unconstrained phase randomization in the transformed domain, hence we define a Hermitian Laplacian matrix that models the graph topology, whose eigenvectors form the basis of a complex graph Fourier transform. We have shown that the Hermitian Laplacian matrix may have negative eigenvalues. We also show in the paper that preserving the graph spectrum amplitude implies several invariances that can be controlled by the selected Hermitian Laplacian matrix. The interest of surrogating graph signals has been illustrated in the context of scarcity of instances in classifier training.

Computing the Partial Correlation of ICA Models for Non-Gaussian Graph Signal Processing.

Conventional partial correlation coefficients (PCC) were extended to the non-Gaussian case, in particular to independent component analysis (ICA) models of the observed multivariate samples. Thus, the usual methods that define the pairwise connections of a graph from the precision matrix were correspondingly extended. The basic concept involved replacing the implicit linear estimation of conventional PCC with a nonlinear estimation (conditional mean) assuming ICA. Thus, it is better eliminated the correlation between a given pair of nodes induced by the rest of nodes, and hence the specific connectivity weights can be better estimated. Some synthetic and real data examples illustrate the approach in a graph signal processing context.

Probabilistic Distance for Mixtures of Independent Component Analyzers.

Independent component analysis (ICA) is a blind source separation technique where data are modeled as linear combinations of several independent non-Gaussian sources. The independence and linear restrictions are relaxed using several ICA mixture models (ICAMMs) obtaining a two-layer artificial neural network structure. This allows for dependence between sources of different classes, and thus, a myriad of multidimensional probability density functions can be accurate modeled. This paper proposes a new probabilistic distance (PDI) between the parameters learned for two ICAMMs. The PDI is computed explicitly, unlike the popular Kullback-Leibler divergence (KLD) and other similar metrics, removing the need for numerical integration. Furthermore, the PDI is symmetric and bounded within 0 and 1, which enables its use as a posterior probability in fusion approaches. In this paper, the PDI is employed for change detection by measuring the distance between two ICAMMs learned in consecutive time windows. The changes might be associated with relevant states from a process under analysis that are explicitly reflected in the learned ICAMM parameters. The proposed distance was tested in two challenging applications using simulated and real data: 1) detecting flaws in materials using ultrasounds and 2) detecting changes in electroencephalography signals from humans performing neuropsychological tests. The results demonstrate that the PDI outperforms the KLD in change-detection capabilities.

Fusion of Scores in a Detection Context Based on Alpha Integration.

We present a new method for fusing scores corresponding to different detectors (two-hypotheses case). It is based on alpha integration, which we have adapted to the detection context. Three optimization methods are presented: least mean square error, maximization of the area under the ROC curve, and minimization of the probability of error. Gradient algorithms are proposed for the three methods. Different experiments with simulated and real data are included. Simulated data consider the two-detector case to illustrate the factors influencing alpha integration and demonstrate the improvements obtained by score fusion with respect to individual detector performance. Two real data cases have been considered. In the first, multimodal biometric data have been processed. This case is representative of scenarios in which the probability of detection is to be maximized for a given probability of false alarm. The second case is the automatic analysis of electroencephalogram and electrocardiogram records with the aim of reproducing the medical expert detections of arousal during sleeping. This case is representative of scenarios in which probability of error is to be minimized. The general superior performance of alpha integration verifies the interest of optimizing the fusing parameters.

Semi-supervised Bayesian classification of materials with impact-echo signals.

The detection and identification of internal defects in a material require the use of some technology that translates the hidden interior damages into observable signals with different signature-defect correspondences. We apply impact-echo techniques for this purpose. The materials are classified according to their defective status (homogeneous, one defect or multiple defects) and kind of defect (hole or crack, passing through or not). Every specimen is impacted by a hammer, and the spectrum of the propagated wave is recorded. This spectrum is the input data to a Bayesian classifier that is based on the modeling of the conditional probabilities with a mixture of Gaussians. The parameters of the Gaussian mixtures and the class probabilities are estimated using an extended expectation-maximization algorithm. The advantage of our proposal is that it is flexible, since it obtains good results for a wide range of models even under little supervision; e.g., it obtains a harmonic average of precision and recall value of 92.38% given only a 10% supervision ratio. We test the method with real specimens made of aluminum alloy. The results show that the algorithm works very well. This technique could be applied in many industrial problems, such as the optimization of the marble cutting process.

Blind detection of nonlinearities in multiple-echo ultrasonic signals.

In this paper, we propose and analyze by means of simulations the use of surrogate data algorithms for blind detection of nonlinearities in multiple-echo ultrasonic signals. We assume a blind scheme so that no information about the input (emitted ultrasonic pulse) can be used. The metrics and equations that model some nonlinear situations are carefully reviewed. Also, closed form equations of the third-order metrics from a simplified second-order Volterra kernel are derived. Computer simulations show that the surrogate data technique is a potentially powerful tool for blind detection of nonlinearities in multiple-echo ultrasonic signals if adequate metrics are chosen. They also reveal interesting trade-offs among parameters that model ultrasonic systems and detection percentages.